Article
Full entry |
PDF
(0.5 MB)
Feedback
PDF
(0.5 MB)
Feedback
Keywords:
stable homotopy; equivariant; fibrewise
stable homotopy; equivariant; fibrewise
Summary:
In this paper, we show how certain “stability phenomena” in unpointed model categories provide the sets of homotopy classes with a canonical structure of an abelian heap, i.e. an abelian group without a choice of a zero. In contrast with the classical situation of stable (pointed) model categories, these sets can be empty.
References:
[1] Bergman, G.M., Hausknecht, A.O.: Cogroups and co-rings in categories of associative rings. Math. Surveys Monogr., vol. 45, American Mathematical Society, Providence, RI, 1996. DOI 10.1090/surv/045 | MR 1387111 | Zbl 0857.16001
[2] Čadek, M., Krčál, M., Matoušek, J., Vokřínek, L., Wagner, U.: Extendability of continuous maps is undecidable. Discrete Comput. Geom. 51 (2014), 24–66. DOI 10.1007/s00454-013-9551-8
[3] Čadek, M., Krčál, M., Vokřínek, L.: Algorithmic solvability of the lifting-extension problem. Preprint, arXiv:1307.6444, 2013.
[4] Goerss, P.G., Jardine, J.F.: Simplicial homotopy theory. Birkhäuser Verlag, 1999. MR 1711612 | Zbl 0949.55001
[5] Hirschhorn, P.S.: Model categories and their localizations. Math. Surveys Monogr., vol. 99, American Mathematical Society, 2003. MR 1944041 | Zbl 1017.55001
[6] Mather, M.: Pullbacks in homotopy theory. Canad. J. Math. 28 (1976), 225–263. DOI 10.4153/CJM-1976-029-0 | MR 0402694
[7] nLab entry on “heap”, http://ncatlab.org/nlab/show/heap</b> tp://ncatlab.org/nlab/show/heap.
[8] Stephan, M.: Elmendorfs theorem for cofibrantly generated model categories. Preprint, arXiv:1308.0856, 2013.
[9] Vokřínek, L.: Computing the abelian heap of unpointed stable homotopy classes of maps. Arch. Math. (Brno) 49 (5) (2013), 359–368. DOI 10.5817/AM2013-5-359 | MR 3159334
Search
Partner of
